NUMERICAL SOLUTION OF NON-LINEAR PARTIAL DIFFERENTIAL EQUATION - FLOW IN A SQUARE CAVITY

Abstract

This project focuses on solving a non-linear partial differential equation that models fluid flow within a square cavity. The problem describes how a fluid moves and conserves mass and is based on the steady-state Navier-Stokes equations and the equation of continuity. We employ a numerical approach based on the finite difference method to solve these equations. The proposed method transforms the complex partial differential equations into simpler algebraic equations, which we solve using computational techniques. Moreover, we analyze fluid behaviour inside the cavity by observing the streamlines that trace the paths of the fluid particles. In addition, we present numerical results and illustrations for different values of the Reynolds number—a measure that describes the relative importance of fluid inertia versus viscosity. As the Reynolds number increases (indicating less viscous fluid), the flow becomes faster and more complex. These observations help us better understand the impact of viscosity on fluid flow in enclosed spaces.